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-   -   to find the exact solution of 1D Burges Equation (https://www.cfd-online.com/Forums/main/6103-find-exact-solution-1d-burges-equation.html)

Tian Baolin May 11, 2003 06:17

to find the exact solution of 1D Burges Equation
 
the Eq. u,t+u*u,x=0 u(x,0)=alpha+Pi*sin(Pi*x),-1<x<1

the analytic solution?

thanks!

Tom May 12, 2003 05:33

Re: to find the exact solution of 1D Burges Equati
 
If you mean the inviscid burgers equation (u_t + uu_x =0) then the solution is, parametrically,

u = U(s) = alpha + pi.sin(pi.s),

x = s + t.U(s)

Tian Baolin May 12, 2003 09:13

Re: to find the exact solution of 1D Burges Equati
 
Dear Tom, Thanks a lot for your solution.Yeah,I just need the solution of inviscid burgers equation.I am sorry that I had given a poor expression of my issue. Your reply is of much help for me,but could you give me a detailed explaination for me. I can't understand meanings of 's'and 'U(s)'. Thanks Again!

Yours sincerely Tian Baolin

Tom May 13, 2003 05:34

Re: to find the exact solution of 1D Burges Equati
 
s is simply a parameter if you fix t and vary s you get the values of u and corresponding values x. Another way of looking at it is to think os s as a Langrangian marker for a fluid particle. If you fix s and vary time the value of u does not change and so is equal to it's initial value U(s) while it's position (x=s at t=0) has changed due to convection.

Hope this helps - you may want to look at the book

"Linear and Nonlinear Waves" by G.B. Whitham

which discusses the Burger equation in detail,

Tom.


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